Hi! We're Elizabeth, Elizabeth and Katrina, and here's our write-up of the Hadley circulation portion of our general circulation project.
Introduction
Hadley circulation works to transport heat from the warm equator to midlatitudes. The Hadley Cell consists of warm air rising from the equator and moving poleward to 30ºN and 30ºS where it falls to the surface. Due to the Coriolis effect which turns winds to the right in the Northern Hemisphere and to the left in the Southern Hemisphere, this air moves westward at the equator and eastward in the midlatitudes around 30ºN and 30ºS.
Source: "Atmosphere, Ocean, and Climate Dynamics: An Introductory Text" by John Marshall & Alan Plumb (2007).
Tank Experiment
To better understand Hadley circulation, a tank experiment was set up to mimic these atmospheric conditions in a controlled environment. A metal container filled with ice was placed in the center of a slowly rotating circular tank. The low rotation rate, 1.28 RPM, and correspondingly low Rossby number (f = 2Ω) was chosen to replicate the low latitude regions where the Hadley Cell forms. Five thermometers (labelled A through E) were placed on the outside of the ice bucket and along the sides and bottom of the plastic tank, in order to measure the generated temperature gradient.
Surface Flow:
Particle tracking software was used to track the motion of paper dots on the surface of the water, in order to determine how velocity varied as a function of distance. The tracks of the five particles studied, along with the plot of their velocities (in meters per millisecond) as a function of distance from the center of the tank, are included below. These surface flows in the tank correspond to the trade winds on Earth.
Thermometers B (at the bottom of the outer wall of the ice bucket) and C (on the bottom of the tank) clearly measure much colder temperatures than sensors placed elsewhere. The maximum temperature gradient recorded between B and D, both near the bottom of the tank, is roughly 5.5K The maximum gradient found at the top of the tank is .5K. Averaging these gives an approximate temperature gradient of 3K over the 18 cm region, or 16.67 K/m.
We can recall the thermal wind equation for an incompressible fluid that we derived in our study of fronts:
This relationship relates the fluid horizontal speed in the tank to the tank’s rotation rate and temperature gradient. By plugging in the calculated value for the ∂T/∂r term into this thermal wind relation, we can try to approximate the velocity at the bottom of the tank. Integrating both sides of the equation, we find:
where u(z1) is the average velocity of a particle traveling on the surface of the water (8.5E-2 m/s for this experiment), u(z2) is the average velocity of a particle traveling near the bottom of the tank (assumed to be roughly 0), and Δz is the depth of water in the tank, here roughly 10cm. Plugging in these values, we find that the expected velocity of a particle traveling at the surface of the tank is:
This result is within the same order of magnitude as the observed values of roughly 8.5E-2 m/s. The slight differences are probably due to the inaccuracy of approximating the temperature gradient as the average of the difference at the top and the difference at the bottom. In reality, the temperature gradient was only observed at around the bottom fifth of the tank, but we didn’t have enough thermometers to measure this precisely.